Pushing the Limits in Sequential Sorting

With refinements to the WEAK-HEAPSORT algorithm we establish the general and practical relevant sequential sorting algorithm RELAXED-WEAK-HEAPSORT executing exactly ndlog ne#2 dlog ne + 1 # n log n # 0:9n comparisons on any given input. The number of transpositions is bounded by n plus the number of comparisons. Experiments show that RELAXED-WEAK-HEAPSORT only requires O(n) extra bits. Even if this space is not available, with QUICK-WEAK-HEAPSORT we propose an efficient QUICKSORT variant with n log n+0:2n+ o(n) comparisons on the average. Furthermore, we present data showing that WEAK-HEAPSORT, RELAXED-WEAK-HEAPSORT and QUICKWEAK-HEAPSORT beat other performant QUICKSORT and HEAPSORT variants even for moderate values of n